The 600 Gal centerline tank (Sgt Fletcher and MDD) did not have a pylon attached. The tank was mounted to the centerline bomb rack and then sway braces were snugged down to the tank. A fairing was then placed around the top poration of the tank. It had two sway brace fins located on the rear of the tank to help stabilize it in flight. It did mount nose down which was to help in seperation when jettisoned.
The 600 Gal High Speed tank was an adapted F-15 tank. It had a brace on the rear to stabilize the tank in flight. It did not have a fairing installed around the tank and you could see a gap at the top. All F-4G's used this type of tank.
Berny
Phormer Phantom Phixer 
On the bench
TF-102A Delta Dagger, 32nd FIS, 54-1370, 1/48 scale. Monogram Pro Modeler with C&H conversion.
Revell F-4E Phantom II 33rd TFW, 58th TFS, 69-260, 1/32 scale.
Tamiya F-4D Phantom II, 13th TFS, 66-8711, 1/32 scale. F-4 Phantom Group Build.